Does the pulse have always the same length? In this case a monoflop can be used which is triggered by the original pulse and troggers the re-generation of a new pulse after the delay.
If the pulse has a varying duration, a shift register (for digital signals) can be used to delay the pulse. The resolution and the max. delay can be controled by the length of the shift register and the clock frequency.
If the puls is analog, if can be digitized by an A/D converter and teh resulting digital data can be delayed by a shift register. At the end of the shift register a D/A converter can reconstruct the analog signal.
A microcontroller with a ring-buffer realized in software can be used instead of a shift register.