I'm trying to update status of Vendor return authorisation using workflow. But status is not updated. How we can achieve this?

process a Item Fulfilment or Close the RTV or some other relevant transaction

Are you perhaps using the Approval Status field in the workflow? I've learned the hard way that using that field requires you to turn on the appropriate checkbox in Accounting Pref>Approval Routing although it's selectable in the workflow. Although on my end VRA doesn't seem to be one of the choices there.

@blue By default approval is not available for VRA. But by default status field is available in VRA. I need to update that field using suite flow.

I haven't tried doing a workflow for VRA so I can't be sure if the Status field is the right field. It can get confusing because there's also an 'Order Status' field(heck in my test account I have two Approval Status fields with the same exact name). From what status to what status are you specifically trying to do?

I need to update pending approval to approved.

Check out SuiteAnswer Id: 96709. It looks like you should try the Order Status field instead.