Reverse charge on renting of immovable property to a bank

If rent is below 20Lakh per annum then no need to charge GST directly or RCM basis.

No RCM under GST over rental charges.......

CBIC has notified that the provisions relating to Reverse Charge Mechanism (RCM) under GST, i.e. under Section 9(4) of the CGST Act, 2017, Section 5(4) of the IGST Act, 2017 and Section 7(4) of the UTGST Act, 2017 have been further Deferred/ Suspended by Govt. by 1 year, i.e. from 30 Sept. 2018 to 30 Sept. 2019. Earlier, the CBEC/ CBIC had notified on 13 Oct. 2017/ 23 March 2018/ 29 June 2018 that implementation of RCM under GST has been deferred upto 31 March 2018/ 30 June 2018/ 30 Sept. 2018 respectively.

Was there any such (like rcm) provision under the service tax Act previously?

Not for renting services.

However wef 01.04.2016 these services were covered under forward charge vide N8/2016-ST dated 01.03.2016