A noun meaning the 'elision' of whole words rather than sounds [ellipsis]
Elision refers to dropping sounds or syllables from words.
What is a similar term (noun) for dropping words from a phrase?
Example
I will give you a period of time lasting from now until 10 February to complete this task.
I will give you until 10 February to complete this task.
Because of idiom and familiarity we can drop the direct object of "to give", which would have been "a period of time" - it's understood.
Solution 1:
The word you might be thinking of is ellipsis.
Removing parts of the (subordinate) adverb clause of time "a period of time lasting from now until 10 February..." seems like a good example of an elliptical adverb clause which is just an adverb clause (one that answers a "where", "when", "how", etc. question) with one or more words removed that can be inferred by context.