"Senior member" is the better choice, unless you're deliberately using it in a joking way.
Although it's technically true that the user's account is older than yours, "elder" is generally used in a more narrow sense to describe someone's actual, real-life age, while "senior" is much more commonly used in this context and doesn't necessarily indicate an age difference.
"Experienced user" or "veteran user" might also be good choices, depending on the exact tone you're going for.
Edit: As others have pointed out, "senior" is often used to indicate not only a longer period of membership, but a higher rank and greater perceived authority within the community.
If you simply want to express that someone's been a registered user of the site for a long time, then "long-standing" or "long-time member" might be a better option.
ell.stackexchange.com/users/118082/pinkfrosty
Given that a young member could have been here for longer than an older person, or someone might have been here for a long time but not achieved many privileges, I suggest long-standing member.
This has no implications of age, superiority or of anything else except purely the time they have been on the site.
ell.stackexchange.com/users/21249/chasly - reinstate Monica
A person might be in their twenties but be a member of a Stack exchange site for as many as 8 years.
In that case, elder or senior member sounds a bit of a misnomer.
I prefer veteran user ( a person who has had long experience in a particular field. )
hi-rep user (only applicable
if the user does indeed have >5K or if the site is large >10K in reputation) See also @pinkfrosty's answer
ell.stackexchange.com/users/1694/Mari-Lou A
(See Edit section at the bottom as well.)
For your situation, senior member is correct and is much better than elder member .
If senior is used like an adjective, in situations like this, it usually means that someone has been with the company/site longer, that they have a higher rank, or something else like that.
This includes someone who has been using SE longer than you.
However senior can also be a noun.
It is a polite way to say old person .
Elder is usually also a noun.
It often means one of the oldest people in the group .
At other times though, it sometimes means an older member of the group, whose specific job/role is to advise and/or to lead .
You can also say elder ly member , which is a polite way to say old member .
Old member means the same thing as member who is old .
Elder member , however, typically means member who is an elder - which is similar to, but slightly different than member who is old .
senior (adjective) : having a higher rank, being with the site/company longer, or something similar old senior member (noun phrase) : member who has a higher rank, has been with the site/company longer, or something similar senior (noun) : old person
elder (noun) : one of the oldest people in the group an older member of the group, whose specific job/role is to advise and/or to lead elder member (noun phrase) : a member who is an elder elderly (adjective) : old elderly member (noun phrase) : a member who is old EDIT:
As was stated in the comments at one point in time, something closer to chasley - reinstate Monica's answer would be much better for Stack Exchange.
Senior member technically works, but Stack Exchange doesn't usually call it that.
Think of a job.
Different people have different titles, and the same job might have different titles at different companies.
For example, one company might use the word teacher , while another uses the word instructor .
Both are technically correct, but each organization has its own preferences.
The same applies for things like senior member .
It technically works for Stack Exchange, but it's a little ambiguous; and long-standing member , as @chasly-reinstateMonica suggested, is fairly unambigous and is much more appropriate for this group.
ell.stackexchange.com/users/4427/Panzercrisis
Realistically, both elder and senior are going to bother someone, eventually, as ageism.
Even "long-time" has that feel to it.
I try to pick something that's inherently a compliment to them instead.
I personally like more tongue in cheek descriptions like superior , ranking , eminent , ascendent , or tenured .
Tenured Member is hard for an experienced forum resident to take the wrong way, since its meaning is inherently respectful of high skill rather than being an age related reward.
There are many such complimentary words people use for sovereignty that can work.
Those only come off as demeaning if someone thinks you're being sarcastic, which is at least easy to correct when it happens.
(There's a reason Can't tell if serious or joking is a popular meme ))
ell.stackexchange.com/users/120303/Greg Smith
Personally, I'd assume "elder member" was meant in the same context as "elder statesman" Collins : An experienced and respected member of an organization or professionis sometimes referred to as an elder statesman
I certainly wouldn't take it as referring to somebody as elderly, or in any way offensively.
That said, I can see how some people might not make that distinction.
As per other answers, senior or long-standing might be safer.
ell.stackexchange.com/users/40759/Mohirl
Questions:   Can I refer to a person who has been using SE for a longer period of time than me as an  elder member ?   Is the usage of  senior member  correct?    Note:  Thanks for the good answers. I asked this  assuming  the word  elder  is applicable in terms of seniority as well, not necessarily physically older as written in  The Free Dictionary .   elder  adj.   Greater than another in age or seniority.   Archaic  Superior to another or others, as in rank.
Can I refer to someone as "elder member" in internet forums?
ell.stackexchange.com
<word-usage>
ell.stackexchange.com/questions/256720
ell.stackexchange.com/users/116056/Severus Snape
Although it's technically true that the user's account is older than yours, "elder" is generally used in a more narrow sense to describe someone's actual, real-life age, while "senior" is much more commonly used in this context and doesn't necessarily indicate an age difference.  If  senior  is used as an adjective, in situations like this, it usually means that someone has been with the company/site longer, or that they have a higher rank.  For your situation,  senior member  is correct and is much better than  elder member. “Senior member" is correct in this context.
“Senior member" is correct in this context.