Female animal, deer or elk, primarily (3)
I believe the answer is:
doe
'female animal' is the definition.
(a female deer)
'deer or elk primarily' is the wordplay.
'primarily' indicates taking the first letters.
The first letters of 'deer or elk' is 'DOE'.
(Other definitions for doe that I've seen before include "possible mate for Rudolph?" , "Female hare" , "Female creature" , "She's a deer" , "Ode to a female rabbit" .)