Foremost of idiots on speed makes you angry (5)
I believe the answer is:
irate
'angry' is the definition.
(irate can mean angry or annoyed)
'foremost of idiots on speed' is the wordplay.
'foremost of' indicates taking the first letters.
'on' is a charade indicator (letters next to each other).
'speed' becomes 'rate' (the speed at which something happens).
The initial letter of 'idiots' is 'i'.
'i'+'rate'='IRATE'
'makes you' is the link.
(Other definitions for irate that I've seen before include "A tier (anag)" , "Angry - furious" , "Extremely angry" , "Angry and incensed" , "Hacked off" .)