HRA Exemption

1. Form 16 is just an acknowledgment and it is not your final computation. If the company has not considered HRA, then the same can be claimed in your IT return provided all the conditions attached to sec 10(13A) relation to HRA exemption is fulfilled. 
2. Sec 10(13A) allows the assessee to claim HRA from the lower of the following,
i) 50 % of the salary (or)
ii) Actual HRA received (or) 
iii) Actual rent paid less 10% of the salary 
In the case of non-metro cities, the above 50% shall be substituted by 40% 
3. Make sure to have proper documents and other computation sheets for future references and for other purposes.
4. In conclusion, HRA exemption u/s (13A) can be claimed relating to your former employer. 
Please correct me if the above solution has an alternative view.