the "car" bit is FORD = anagram of has gives ASHFORD ... the nickname of this club is the ASHTREES for which you have the defn at the beg....I think suspension is the extra word.
The 12 specials are symmetric in the grid so that should help
Turast has given a parse for 15a ... look up
17a pirates is the defn . woodwork is the extra word. teacher = don + anagram of crates ... gives Doncaster whose nickname is the ROVERS