Can my ex-spouse whom I'm paying maintenance/alimony for claim from my Estate?

Presuming that you are currently paying alimony/maintenance to your ex-spouse, it will then depend on whether the maintenance order is secured or unsecured.

Specifically:

Duration of orders for maintenance

117.  Except where an order for maintenance is expressed to be for any shorter period or where any such order has been rescinded, an order for maintenance shall expire —

(a) if the maintenance was unsecured —

(i) on the death of either spouse or former spouse;

(ii) in the case of maintenance payable to a former wife, upon her remarriage; or

(iii) in the case of maintenance payable to an incapacitated former husband, upon his remarriage; or

(b) if the maintenance was secured —

(i) in the case of maintenance payable to a wife, on her death;

(ii) in the case of maintenance payable to a former wife, on her death or upon her remarriage;

(iii) in the case of maintenance payable to an incapacitated husband, on his death; or

(iv) in the case of maintenance payable to an incapacitated former husband, on his death or upon his remarriage.

Source: Singapore Women's Charter

Additionally, if you have failed to make prior payments, it will be like a debt in which case she can.

If you have genuine legal concern on this, you might want to consider consulting a lawyer via the " Consult Lawyer" function accordingly. (charged separately)