The best place to store your luggage in Delhi is the Cloak room at the railway station. All you need is a connecting train ticket. Even if you are not travelling by train at any time, get a cheapish train ticket to be able to store your gear in the cloak room. I have done this several times while transiting through cities. Hassle free and super convenient. Alternatively, several hostels in Delhi will be able to help you with luggage storage (for free or at a nominal price). Madpackers is one good option. Get in touch with them and discuss in advance, so they can make any necessary arrangements, if needed.
Hi Vishal! In Pahar Ganj area, which is very close to New Delhi Station, there are many Luggage storage facility providers. Some of trusted are - Ajay's Hotel The Anoop Hotel, Main Bazaar Luggage Room, T-302 Main Bazar
There are cloakroom facilities in the railway station, but they won't accept your gear if you do not have locks and you can keep them for a max period of 7 days. Cloakroom at the airport will also not accept bags which are not locked and are costly (Rs 600 per bag!) You can keep your bags at one of GoLuggageFree's (www.goluggagefree.com) luggage lockers facilities. Their locations have CCTV security and a person who keeps an eye out for your luggage throughout. In addition, they provide you with locks and cost around the same price as a railway station cloakroom. Hence, you should be able to store your gear without any issues. I've used their luggage storage space close to New Delhi Railway station and found it really useful. They have luggage lockers throughout Delhi. You will need to check their website and app for more details on it. Hope this helps.