A method performed by a UE for implementing a random access procedure is provided. The method transmits a MSGA, monitoring an MSGB-RNTI within an MSGB time window starting from an earliest symbol of an earliest PDCCH occasion after the MSGA transmission. The method receives the MSGB in a first slot. The MSGB includes a success RAR that contains a HARQ Feedback Timing Indicator, a Physical Uplink Control Channel (PUCCH) Resource Indicator, and a UE Contention Resolution Identity. The method determines, by a MAC entity of the UE, to instruct a lower layer to transmit a HARQ feedback in a second slot in response to the reception of the success RAR. The method delivers, by the MAC entity, the HARQ Feedback Timing Indicator and the PUCCH Resource Indicator to the lower layer, and performs, by the lower layer, a HARQ feedback delivery on an uplink (UL) resource.