I had Ascendas H-Trust REIT and now that Capitaland has completed the acquisition, what happens to the shares that I previously purchased?

First of, congrats to us (I have some as well) because Ascott REIT is going to acquire all of AHT's shares at $1.08 and since IPO till date, AHT has never reached that price, hence its definitely beneficial to AHT's unitholders.
They will do this via provision of shares from Ascott REIT-Business Trust (the combined entity following the M&A) and cash as mentioned by Darren :)

However, this is with the assumption that Ascott REIT's price is at $1.30. Therefore, if Ascott REIT's price begins to decline, then the worth of AHT holdings would be less than $1.08. Therefore, a lot is dependent on how Ascott REIT performs

Ascott Reit acquiring all the A-HTRUST Stapled Units for a consideration of S$1.0868 per A-HTRUST Stapled Unit, comprising S$0.0543 in cash and 0.7942 Ascott Reit-BT Stapled Units issued at a price of S$1.30.

you may want to refer to this presentaion slide for the detail and timeline.

https://ir.a-htrust.com/newsroom/20190703_07330...