HRA from one employer but not from the other

Since the previous employer did not deduct tax for the few months worked with them, you can now liable to pay some amount as tax. To reduce the liaility, you can claim deductions available under various sections of the Income tax Act, such as Section 80C for investments in PPF, NPS, etc.,or Section 80D for health insurance premiums.

My actual question is "While filling ITR, how should I exempt the rent that I paid during the last financial year?"

Should I claim HRA from one emplyer and rental paid for the rest of the period (with other employer)?