Take on PM playing around with mistress? (4,5)
I believe the answer is:
kept woman
'mistress?' is the definition.
(synonyms)
'take on pm playing around with' is the wordplay.
'playing' is an anagram indicator.
'around' means one lot of letters goes inside another.
'with' becomes 'w' (short for with).
'take'+'on'+'pm'='takeonpm'
'takeonpm' is an anagram of 'keptoman'.
'keptoman' enclosing 'w' is 'KEPT WOMAN'.
(Other definitions for kept woman that I've seen before include "Maintained female" , "Mistress" .)