Can I apply for a trademark if an other application exists with similar (not identical) name in "Objected" status?

For application there are no limitations. One can apply for trademark even similar application is already in existence. But an objection can be raised by Ministry under relative grounds. In such objection one needs to reply for the same. According to ACT even if you are applying for trademark registration at later stage then also you will get the first preference for the registration. Hence if one has proofs that he is using that brand before other, then he can claim benefit of prior user.