She'll back saintly Irishman up (5)
I believe the answer is:
nadia
'she'll' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.
'back saintly irishman up' is the wordplay.
'back' becomes 'aid' (I've seen this in another clue).
'saintly irishman' becomes 'an' (I can't justify this - if you can you should believe this answer much more).
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'aid'+'an'='aidan'
'aidan' reversed gives 'NADIA'.
Can you help me to learn more?
(Other definitions for nadia that I've seen before include "Russian woman" , "___ Comaneci, Romanian-born American gymnast" , "Miss" , "(Originally Russian) female name (reverse of Irish male name)" , "Name of girl" .)