I saw a sentence like this:
Wilkinson is contesting the release, and threatened to sue should it be released.
I could understand it but do you know what do they call this kind of use of "should" in grammar?
This use of "should" appears to be called expressing the conditional mood. The New Oxford American Dictionary describes it in the following way:
(formal) expressing the conditional mood
- (in the first person) indicating the consequence of an imagined event:
if I were to obey my first impulse, I should spend my days writing letters
- referring to a possible event or situation:
if you should change your mind, I'll be at the hotel
should anyone arrive late, admission is likely to be refused
(I added emphasis to the part most relevant to your question.)
Often, at least to my ear, this use of "should" carries a connotation of improbability. Example:
In the [unlikely] event that you should need to complain, please email the management team directly.
I found a nice answer as below:
These two sentences are very similar in meaning. But 'Should you have...' or 'If you should have...' may be used in preference to 'If you have...' if we want to suggest a slight possibility of something happening or when we are making suggestions or giving advice. Compare:
'If you have any free time, make sure you visit the old town.' (It's possible, or even likely, that you may have some free time.)
'If you should have any free time, make sure you visit the old town.' (I don't really expect you will have any free time, but if you do...)
'Should you fail this exam, you can always re-take it next year.' (I think it's unlikely, but it's possible you may fail it and if you do...)
'If you fail this exam, you can always re-take it next year.' (I'm just pointing this out to you. I don't have a strong opinion on the matter one way or the other.)
The if is simply elided: “If you should have any questions . . . .”
Should you have any questions, please call
means the same as
If you have any questions, please call
but the former is more formal. Here should is used as a modal verb with the sense of possibility.