What is acclimation process of elections?

I think the term you're looking for is acclamation. The process varies slightly by each organization that conducts elections, but here it is in a nutshell...

The nomination period runs it's normal course - usually weeks, or months

One person comes forward and fills out the appropriate paperwork / appropriate processes

No other persons come forward to contest the position

The nominations close at a preset time

The Clerk or entity overseeing the election inspects the paperwork and satisfies themselves that everything is in order

The Clerk declares the person who came forward as elected by acclamation. That is, they were the only ones nominated, and now officially are the person elected for that position

The persons title now changes from candidate to position-elect, for example Trustee Candidate to Trustee-Elect

The person takes office on the predefined date.

That's a very long explanation for something that boild down to 'no one else came forward'

Cheers