catch up works fine in this case as well, but with a different preposition: on instead of with .
See e.g. the examples given by The Free Dictionary : To do a task that one has neglected.
If you haven't done any biology homework in weeks, you better spend this weekend catching up on it—it's due on Tuesday!
I'm trying to catch up on work after being out sick, but my inbox alone might take all day!
ell.stackexchange.com/users/18673/Glorfindel
Yes, "to catch up" means "to make up a difference."
Although the verb is based on the verb "to catch," which primarily has a physical sense, and although "to catch up" in the sense of pulling even after having been physically behind is a meaning in common use, "to catch up" is also commonly used in a more figurative sense.
"Your daughter is behind due to her having been ill and missed so many classes, but I am confident that she can catch up if she does some extra work" is a perfectly good sentence in American English.
ell.stackexchange.com/users/64237/Jeff Morrow
... to work more than usual ...
We will have to work overtime to meet the deadline.
We will have to put in some long hours to meet the deadline.
ell.stackexchange.com/users/10264/Tᴚoɯɐuo
Less succinct than catch up is make up for lost time .
From Dictionary.com : Also, make up ground .
Hurry to compensate for wasted time, as in They married late but hoped to make up for lost time , or We're behind in the schedule, and we'll just have to make up ground as best we can .
The first term was first recorded in 1774; the variant dates from the late 1800s.
ell.stackexchange.com/users/9423/Matt
Elucubrate is a related-but-advanced word that roughly means 'produce after burning the midnight oil [to catch up]'.
Nobody but the most advanced literature majors will understand you though.
ell.stackexchange.com/users/86791/Aaron Bell
"Working double time" is a one saying I use, don't know of any exclusive verbs.
ell.stackexchange.com/users/86829/Dylan
Imagine one is behind schedule and then decides  to work more than usual to compensate the delay, or the difference between where he is and where must be . Do you have a word or expression or phrase equivalent with the italic part?  In a hiking group, those who fall behind try and  catch up  with others. It looks as though  catch up (with)  is typically used with people, can we use it with plan, schedule, lessons etc.?
Verb meaning "compensate for falling behind schedule by working more"
ell.stackexchange.com
<word-request><vocabulary>
ell.stackexchange.com/questions/189874
ell.stackexchange.com/users/3630/Juya
"To catch up with" is commonly used in this context. "To work overtime/double time" or "to put in long hours" could also be used. Catch up with/on' is a valid phrase in this context, meaning 'make up a difference'. Other common phrases include 'work overtime', 'put in long hours' or 'work double time'.
Catch up with/on' is a valid phrase in this context, meaning 'make up a difference'. Other common phrases include 'work overtime', 'put in long hours' or 'work double time'.