Woman with small part to tweak (5)
I believe the answer is:
adapt
'to tweak' is the definition.
(I've seen this in another clue)
'woman with small part' is the wordplay.
'woman' becomes 'ada' ().
'with' says to put letters next to each other.
'small part' becomes 'pt' (abbreviation; 'small' asks for an abbreviation).
'ada'+'pt'='ADAPT'
(Other definitions for adapt that I've seen before include "Become adjusted to new circumstances" , "Adjust to changed circumstances" , "match" , "Change to suit a different purpose" , "Adjust (to changes)" .)