Israel has a complicated relationship with Russia, which it doesn't want to hurt.
Russia is a major supporter of Assad's regime in Syria, which is aligned with Iran and Hezbollah, Israel's bitter enemies ( see here ).
Yet, Russia does not interfere when Israel operates in Syria against them.
Russia is also a significant importer of Israeli produce, as well as a significant source for tourism in Israel.
All in all, Israel has a lot to lose from upsetting Russia, and little to gain.
politics.stackexchange.com/users/14958/ugoren
In January 2010, a team of Israeli government agents travelled to Dubai, UAE and, in a highly-sophisticated operation, assassinated a senior official of the terrorist organization Hamas.
Dubai police were able to describe the operation by piecing together surveillance videos, which were released to the public.
Israel was subject to widespread international condemnation for the attack.
Many countries responded to Israel with warnings, threats, arrest warrants and/or diplomatic expulsions.
One country with no reaction was Russia.
Now that Russia has conducted a similar operation, Israel may be acting in-kind.
Note: Both Israel and Russia have denied involvement in these operations.
Nothing has been proven in a court of law.
Therefore, the charges against Israel and Russia are mere allegations.
References: https://en.wikipedia.org/wiki/Assassination_of_Mahmoud_Al-Mabhouh https://youtu.be/bJujIwtdk8w
politics.stackexchange.com/users/12464/Michael Benjamin
The action against Russian Diplomats is being led by the UK, not the US.
UK and Israel are not particularly close.
The other countries that have supported the UK are Countries with a close relationship with the UK:
EU allies, Commonwealth allies or Nato allies.
Israel is none of these.
Israel has a complex relationship with Russia.
It's not clear that the UK or her allies even asked Israel to act against Russia.
politics.stackexchange.com/users/8554/James K
Israel's prime minister has a thin majority which includes the far-right and Russian-speaking Lieberman , who is minister of defense .
His party historically gets most votes from Russians in Israel, who like Putin.
Since Lieberman entered the government around 2009, Israel has cozied up a lot with Russia.
Some context: https://en.wikipedia.org/wiki/Thirty-fourth_government_of_Israel#Cabinet_members https://en.wikipedia.org/wiki/Avigdor_Lieberman
https://en.wikipedia.org/wiki/Yisrael_Beiteinu
politics.stackexchange.com/users/10455/Nemo
Israel (along with North Korea, South Sudan and Egypt) is not a party to the Chemical Weapons Convention.
Since the UK is treating this as a CWC issue, Israel might not want to bring attention to its own status.
politics.stackexchange.com/users/6890/Keith McClary
After reading all the other answers and researching the Skripal incident a bit more, one possible explanation of Israel's "inaction" has occurred to me: Israel (Mossad) knows that the Russians (the government of the Russian Federation to be exact) was not involved.
This article (pro-Russia source warning!) suggests a possibility of a third party (other than Russia or the UK) being involved in the assassination.
They mention Ukraine, for example.
politics.stackexchange.com/users/9256/ebhh2001
The US and more than 20 other  countries have expelled Russian diplomats  in response to the poisoning of the former Russian spy Sergei Skripal. As of this writing, Israel has not expelled any Russian diplomats in response to this particular incident.    Given that Israel is considered a US ally and is a major  recipient of the US foreign aid , what would be the possible reasons behind Israel's not joining in the effort to punish Russia?
Why has Israel not expelled Russian diplomats in response to the Skripal poisoning?
politics.stackexchange.com
<united-states><russian-federation><israel><foreign-policy><assassinations>
politics.stackexchange.com/questions/30028
politics.stackexchange.com/users/9256/ebhh2001
Israel has a complicated relationship with Russia, which it doesn't want to hurt.  Russia is a major supporter of Assad's regime in Syria, which is aligned with Iran and Hezbollah, Israel's bitter enemies. Israel wants to protect its complicated relationship with Russia since it supports Assad’s regime.
Israel wants to protect its complicated relationship with Russia since it supports Assad’s regime.