It's pleasant embracing an eastern relative (5)
I believe the answer is:
niece
'relative' is the definition.
(type of relative)
'it's pleasant embracing an eastern' is the wordplay.
'it's pleasant' becomes 'nice' (similar in meaning).
'embracing' indicates putting letters inside.
'an eastern' becomes 'e'.
'nice' going around 'e' is 'NIECE'.
(Other definitions for niece that I've seen before include "Daughter of a sibling" , "A sibling's daughter" , "Criminal" , "Brother's daughter" , "Preparation for curdling milk" .)