Woman with small part as tailor (5)
I believe the answer is:
adapt
'tailor' is the definition.
(I've seen this in another clue)
'woman with small part' is the wordplay.
'woman' becomes 'ada' (woman's name).
'with' says to put letters next to each other.
'small part' becomes 'pt' (abbreviation; 'small' indicates an abbreviation).
'ada'+'pt'='ADAPT'
'as' is the link.
(Other definitions for adapt that I've seen before include "match" , "Modify; acclimatise" , "Adjust (to new conditions)" , "Make fit" , "Tailor" .)