Study of the population's pay her dogma almost spoiled (10)
I believe the answer is:
demography
'study of the population's' is the definition.
(study of demographic groups)
'pay her dogma almost spoiled' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'spoiled' indicates anagramming the letters.
'pay'+'her'+'dogma'='payherdogma'
'payherdogma' with its final letter removed is 'payherdogm'.
'payherdogm' is an anagram of 'DEMOGRAPHY'.
(Other definitions for demography that I've seen before include "Study of populations" , "Study of population" .)