New First Lady full of Republican spirit (5)
I believe the answer is:
nerve
'spirit' is the definition.
(nerve is a kind of spirit)
'new first lady full of republican' is the wordplay.
'first' suggests taking the first letters.
'lady' becomes 'eve' (I've seen this before**).
'full of' is an insertion indicator.
'republican' becomes 'r' (abbreviation).
The initial letter of 'new' is 'n'.
'eve' placed around 'r' is 'erve'.
'n'+'erve'='NERVE'
(Other definitions for nerve that I've seen before include "Courage, like bodily fibre" , "Courage - or effrontery" , "Cheek; self-possession" , "Dangerous type of gas" , "Brass neck" .)