What happens when this company goes from the OTC to NYSE?

Without studying the financials and more information about the company it is difficult to gauge investor reaction to the IPO. My guess is that its current price is only a reflection of the news it was planning to go public on the NYSE, since the stock was trading down around $2 prior to November of 2020.

What the offer price is now doesn't mean it won't change (and it can go down or up) prior to the IPO. Just from a brief glance, they're making about 24% of the company's shares available, so there are a LOT of shares held/controlled by company insiders, and that could make it difficult for the stock to do much once those shares are eligible to trade. Basically, for every publicly trading share there will be THREE shares held by company insiders.

EDIT

Here's a good article on what happens when a company moves from the OTC to NYSE

https://www.investopedia.com/ask/answers/08/otc-nyse-nasdaq.asp

I will say that any time a company like this files an S-1 with a 22-page "RISK FACTORS" section it scares the crap out of me. READ THIS SECTION and you will have a good idea of the headwinds this company is facing and how its past is going to work heavily against it (most notably, pension contribution deferrals since 2002, more than $940 million of debt, etc.)

Note that the $10.51 price could be misleading because:

• It is the price of the last trade that happened about two weeks ago (on 2021-04-09).
• The stock is illiquid ($10.00 bid for 100 shares, and no offers).

As @SRiverNet mentioned, the actual IPO price could be different from the estimate of $18 to $20 per share. Indeed, that was what happened. One day before the IPO, the IPO price was reduced to $14 (press release: Agiliti Announces Pricing of Initial Public Offering). The shares opened at $16.05, which is again below the estimate.