19D: Secret store is under stone (5) _T_S_
I think this should be ST / ASH but "...remains under stone" would have been better, unless I'm missing something?
And 11A: Star position of Oman's capital (7,3) L_A_I_G _A_
I can only see "leading man," i.e. the capital 'O' of Oman is leading '...man'