This writer backed Iron Lady in power (7)
I believe the answer is:
empress
'lady in power' is the definition.
'this writer backed iron' is the wordplay.
'this writer' becomes 'me' (the person who wrote the clues).
'backed' says the letters should be written in reverse.
'iron' becomes 'press' (I've seen this before).
'me' in reverse letter order is 'em'.
'em'+'press'='EMPRESS'
(Other definitions for empress that I've seen before include "Maria Theresa, perhaps" , "Female ruler" , "1 across was from 1877" , "Female sovereign" , "She rules over many territories" .)