This is Gajalakshmi. The Gaja (elephants) part is obvious. Lakshmi is identified by the two lotus buds she is holding in her rear/upper hands. Her front hands are in Abhaya and Varada mudra (Protection and boon bestowing).
The four elephants are meant to carry four pots of water for her Abhisekh (ritual bathing). The elephants represent the four cardinal directions and the symbolism is obvious. It is a clever way of showing the four elephants. Some of the other examples on this blog are standing Gajalakshmi and Gajalakshmi on an Elephant.
Gajalakshmi is sitting in Ardhapadmasana on an inverted lotus. The pillars supporting the elephant and the inverted lotus are supported by a rectangular base.
The casting is quite thin. See the edges of the lower rectangular base. It is quite likely this idol is from Tamil Nadu. At some stage the face was re-cut and in that process this idol has lost some of the elegance that one expects from Tamil Nadu bronzes.
The idol is about 7.5 cm in height. Going by the wear one may date it to prior to the eighteenth century.
23 Jan 2019: Krishna, one of the keen followers of this site, pointed out this idol could be one of the of the Mahavidyas, Kamalatmika. The iconography of Kamalatmika is very similar to that of Gajalkashmi.