A registrar may only initiate a transfer if it has obtained a completed Form of Authorization (FOA) from either 1) the registrant or 2) the administrative contact for the domain.
The registrar must be able to produce a copy of this documentation when it is requested. Failure to do so is grounds for reversal of a transfer in the event that a complaint is filed under the Transfer Dispute Resolution Policy.
Thus, the first step should be for your previous registrar to request from the new registrar a copy of the form used for authorizing the transfer. The registrar can then proceed with initiating a dispute as appropriate.
Contact your previous registrar for assistance.