Old, Her Majesty shows some resistance! (3)
I believe the answer is:
ohm
'some resistance' is the definition.
(I've seen this before)
'old her majesty' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'her majesty' becomes 'hm' ().
'o'+'hm'='OHM'
'shows' acts as a link.
(Other definitions for ohm that I've seen before include "physical unit" , "A little resistance" , "measure of resistance" , "Physicist" , "lawmaker" .)