Second mate welcoming Republican like Bush (7)
I believe the answer is:
shrubby
'like bush' is the definition.
(like a bush or shrub)
'second mate welcoming republican' is the wordplay.
'second' becomes 's' (common abbreviation).
'mate' becomes 'hubby' (hubby is a kind of mate).
'welcoming' is an insertion indicator (in sense of 'inviting in').
'republican' becomes 'r' (abbreviation).
'hubby' going around 'r' is 'hrubby'.
's'+'hrubby'='SHRUBBY'
(Other definitions for shrubby that I've seen before include "Covered with bushes" , "Like lilac" .)