Gary hoped desperately to welcome maiden studying this? (10)
I believe the answer is:
demography
'studying this?' is the definition.
(study of populations)
'gary hoped desperately to welcome maiden' is the wordplay.
'desperately' indicates anagramming the letters.
'to welcome' indicates putting letters inside (inserted letters are welcomed in).
'maiden' becomes 'm' (cricket abbreviation).
'gary'+'hoped'='garyhoped'
'garyhoped' is an anagram of 'deography'.
'deography' placed around 'm' is 'DEMOGRAPHY'.
(Other definitions for demography that I've seen before include "Study of population" , "Study of populations" .)