Hi Maik,
Thanks for replying....
So, As per your thought. New Index consumes database space and is not recommended to proceed with this approach, Is that what you meant ?
Observation : After Creating this new Index for that particular query(Slower Transaction query) on the table where the transaction is happening. Despite it took long running operation of nearly 7 hours. Now, the transaction which I am functioning through UI  Acton is really quick. Looks like this resolved the slower transaction process. So Can I promote it to next level Instances and move it to our Main PRODUCTION Instance by capturing the newly created Index ?? Can you refer screenshot attached shows after long running operation. There is a record created under related item "Related Indexes" tab and it is somehow shows relation between my current table where I am working on and to Task table.

Can you please share your thoughts. Thanks