1. If you want to have one signal shifted to another signal, with no conditions or control you can just "connect the wires" properly and there is no hardware required at all.
2. If you want to have one signal shifted to another signal, UNDER some conditions or control you need a MUX to connect the wires in several ways, as you like. You need combinational logic resources (e.g. LUTs). Amount depends on number of bits and number of wiring combinations.
3. If you want the signal to become shifted to itself you need a register and possibly some LUTs, as in 1 and 2 respectively.
4. In case 2, if you have problems with latency, you may need also a register inserted in control and/or data lines.