Delhi's difficulty is not finding a tutor, it is distance. A family in Saket and a tutor in Rohini are most of an evening apart, and the city is large enough that CBSE, ICSE and international-curriculum schools all sit within a few kilometres of each other, so "a Delhi tutor" means very little until you know which end of the city and which board. Home tuition runs in Dwarka, Janakpuri, Pitampura, Rohini, Mayur Vihar, Lajpat Nagar and Vasant Kunj, in person and online.
Distance then decides more than most families expect. A tutor travelling an hour each way for a six o'clock class will hold that slot for a few weeks and then start rescheduling it, so the arrangement that survives a whole year is usually one inside your own corridor — the same stretch of the metro, or a neighbourhood the tutor already teaches in — with online covering anything beyond it. It is a fair thing to ask before you agree anything: where else do you teach, and how are you getting here.
The board question is the other one to raise early, because Delhi is one of the few cities where CBSE, ICSE and an international curriculum can sit on the same street. They set different papers and reward different answers, and a tutor who has taught one for years may never have seen how the other is marked. From Class 11 there is a further split. Undergraduate admission to the central universities here runs through a common entrance test rather than board marks alone, so board preparation and entrance preparation are two separate pieces of work in the same year, and most families hire for one of them rather than for both at once.