Hi all new member here 😀 

Picked up a used 2014 S3 quattro which is making a sort of reverberating sound which appears to be coming from the back left of vehicle. Had DSG and haldex service from garage prior to collection. All tyres seem to be very good. Any help appreciated 👏 

(Back left was initially making a slight grinding noise but has now disappeared. Unsure if related)

I'd take this back to the dealer you bought it from for diagnosis. If bought within the last 39 days the repair should be free 

Not unheard of to have worn wheel bearings. Reverberating sound at 40-50mph is usually tell-tale which alternates on left or right hand corners. Sometimes difficult to determine simply by spinning wheel, even if it spins, with Quattro (AWD). I’ve usually dismantled to rotate the actual hub and get a feel from there. If it is a bearing, the renew in pairs. F.A.G. brand is all I’d fit given labour involved.

You can rule out tyres if you go to a tyre shop, check it’s not lost weights and any tyre flat spot. Grinding could have been corroded brakes if it’s been sitting in the damp for some time.

If car new to you, then VCDS scan worth it for any logged DTC faults.