One from Glasgow hosts peer, good runner (8)
I believe the answer is:
yearling
'runner' is the definition.
(young race horse, something which runs)
'one from glasgow hosts peer good' is the wordplay.
'one from glasgow' becomes 'yin' (Scottish dialect term for 'one').
'hosts' is an insertion indicator.
'peer' becomes 'earl' (earl is a kind of peer).
'good' becomes 'g' (abbreviation).
'yin' placed around 'earl' is 'yearlin'.
'yearlin'+'g'='YEARLING'
(Other definitions for yearling that I've seen before include "Animal 12 months old" , "Young horse" , "Animal in its second 12 months" , "Relaying (anag.)" , "Youngster" .)