Baby rightly ends with the foot soldiers (8)
I believe the answer is:
infantry
'the foot soldiers' is the definition.
(I've seen this before)
'baby rightly ends' is the wordplay.
'baby' becomes 'infant' (synonyms).
'ends' suggests removing the centre.
'rightly' with its centre taken out is 'ry'.
'infant'+'ry'='INFANTRY'
'with' is the link.
(Other definitions for infantry that I've seen before include "Army unit of foot soldiers" , "Men fighting" , "Unmounted fighters" , "fighting group" , "part of the army" .)