Minister that's beginning to spend time in crowd (9)
I believe the answer is:
priestess
'minister' is the definition.
(I know that priestess is a type of minister)
'that's beginning to spend time in crowd' is the wordplay.
'that's' becomes 'ie'.
'beginning to' indicates taking the first letters.
'in' indicates putting letters inside.
'crowd' becomes 'press' (to press can mean to crowd around).
The first letters of 'spend time' is 'st'.
'ie'+'st'='iest'
'iest' going inside 'press' is 'PRIESTESS'.
(Other definitions for priestess that I've seen before include "Female hierophant" , "Woman conducting religious rites" , "Clergywoman" , "Eg, Vestal virgin" , "One in temple possibly" .)