Depends on the kind of request you have... Different TA's may have different takes on how to handle these, but here are mine:

restaurant reservations, tickets, etc. — go directly to the Concierge for these

specific requests for your guestroom including desired welcome amenities, room arrangements, rollaway beds, early check-in or late check-out, upgrades, etc. — Contact your TA for these. Bonus points if you communicate these at the time of the reservation request, so everything can be handled at once!

Specific advice for early check-in requests: hotels always want to know a guest's ETA (estimated time of arrival). Blocking rooms is like a jigsaw puzzle, and this information makes their life easier. So instead of asking for a generic "early check-in," ask for a 1 p.m. early check-in (for example).

airport transfers — Some TA's will book airport transfers through Carey Limousine, etc. However, I always send these requests directly to the hotel's concierge. The biggest advantage to having the hotel arrange transfers is that the front desk will have a good idea in advance of your actual arrival time, and the front desk will be ready for your check-in. The other advantage is that if you cancel your reservation or change your dates, the Concierge [should] get this information from the hotel's reservations team, and any arrangements made in connection with your reservation [should] automatically be cancelled.