Like irrational tirade for an ambitious type (8)
I believe the answer is:
aspirant
'an ambitious type' is the definition.
(someone who aspires)
'like irrational tirade' is the wordplay.
'like' becomes 'as'.
'irrational' becomes 'pi' (an irrational number).
'tirade' becomes 'rant' (both can mean an angry outburst).
'as'+'pi'+'rant'='ASPIRANT'
'for' acts as a link.
(Other definitions for aspirant that I've seen before include "One who wants to succeed" , "Hopeful candidate" , "One works hard to achieve something" , "Partisan sort of hopeful" , "Hopeful one" .)