Hi longbow
From your post I assume that you are in receipt of IR ESA. ESA stops when you reach State Pension age along with any disability premiums that you received with your IR ESA.
You may be entitled to claim Pension Credit along with your SP;
www.gov.uk/pension-credit at the same time you may be eligible to claim SDP depending on your circumstances.
The SDP became payable from the first day that all three of the following applied.
1. You had an award of ESA and we’re receiving or were entitled to receive Income Related ESA or Pension Credit.
2. You had an award of PIP Daily Living.
3. You met the criteria for payment of the SD Premium, namely that you lived alone or were considered to be living alone and no one receives Carers Allowance against your PIP award.
In answer to your question you do not have to be in receipt of IR ESA to claim SDP, you can get SDP if you are eligible to claim PC and meet the qualifying conditions.
Gary