Woman starts to embrace pet ruminant (5)
I believe the answer is:
sheep
'ruminant' is the definition.
(sheep is a kind of ruminant)
'woman starts to embrace pet' is the wordplay.
'woman' becomes 'she' (**).
'starts to' suggests taking the first letters.
The initial letters of 'embrace pet' is 'ep'.
'she'+'ep'='SHEEP'
(Other definitions for sheep that I've seen before include "Dolly or Shaun" , "Eg, a merino" , "Source of mutton" , "Animals said to lack initiative" , "Woolly animals" .)