One quivered behind first of May demonstrator (7)
I believe the answer is:
marcher
'demonstrator' is the definition.
(I've seen this before)
'one quivered behind first of' is the wordplay.
I cannot quite understand how this works, but
'one' could be 'er' (I've seen this in other clues) and 'er' is found within the answer.
'first' could be 'arch' and 'arch' is located in the answer.
A single letter 'm' remains which might be clued in a way I don't understand.
This explanation may well be incorrect...
'may' acts as a link.
(Other definitions for marcher that I've seen before include "who may be protesting?" , "Person demonstrating" , "Frontiersman" , "character needing to keep in step?" , "Border dweller" .)