Word for splitting something into two parts and joining them together using a new element
The best word I can think of for the generic case is splice:
- to join together or unite (two ropes or parts of a rope) by the interweaving of strands.
- to unite (timbers, spars, or the like) by overlapping and binding their ends.
- to unite (film, magnetic tape, or the like) by butting and cementing.
definition from dictionary.com
In your specific examples, a little bit of extra verbage may be required:
We will need to splice an extension into this wire
We're going to splice a pressure meter segment into this run of pipe
This is mostly using sense 3 from the definition above, where we are first creating new ends of our wire or pipe, then joining each end to the new element.
(Because an instruction pipeline is not really physical and has no significant cost for placing a new entry between other entries, "splice" doesn't really seem to apply; simply "inserting" seems fine.)
Many technical subjects in order to reduce ambiguity expect the right word
Tap is perfectly correct for inserting a measurement meter mid way between joints. If opting for a more expensive replacement of the segment with a meter then that's that.
If you need to renew a segment of cable as you would use two splices.
For steel its a single or double spliced joint.
To inject an instruction that's what you need to say you do.
The only form of singular commonality is the above cases is you add an addition. or attach an attachment
You need an intermediation of some kind between the cut pieces.
The word intermediate has a variety of meanings, but they all refer to something in between two other things.