Foremost of idiots on speed makes you angry (5)
I believe the answer is:
'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'.
'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" .)