Cheer up former partner getting to detest bats' lair inside (10)

I believe the answer is:

exhilarate

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'cheer up' is the definition.
'exhilarate' can be an answer for 'cheer' (thesaurus). I'm not certain of the 'up' bit.

'former partner getting to detest bats' lair inside' is the wordplay.
'former partner' becomes 'ex'.
'getting to' means one lot of letters go next to another.
'detest' becomes 'hate' ('hate' can be a synonym of 'detest').
'bats'' indicates an anagram (I've seen 'batted' mean this).
'inside' means one lot of letters goes inside another.
'lair' anagrammed gives 'ilar'.
'hate' placed around 'ilar' is 'hilarate'.
'ex'+'hilarate'='EXHILARATE'

Can you help me to learn more?

(Other definitions for exhilarate that I've seen before include "Make very happy or very animated" , "Enliven" , "Thrill" , "Cheer" .)

I've seen this clue in the Irish Times.

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