Hobby that's irrational entertaining husband recently (9)
I believe the answer is:
philately
'hobby' is the definition.
(I've seen this before)
'irrational entertaining husband recently' is the wordplay.
'irrational' becomes 'pi' (an irrational number).
'entertaining' is an insertion indicator (inviting in, as for dinner).
'husband' becomes 'h' (abbreviation).
'recently' becomes 'lately' (synonyms).
'pi' going around 'h' is 'phi'.
'phi'+'lately'='PHILATELY'
'that's' is the link.
(Other definitions for philately that I've seen before include "The hobby of stamp collecting" , "collecting small items that may grow in value" , "Stamp-collecting" , "Collecting little stickers" , "pursuit" .)