Dueling IRAs

In a word, No. Your new employer has a limited number of investments you can put the money in. Another problem with your question is “an IRA account started with a new employer?” I don’t think your employer offers an IRA.

So you're trying to roll an IRA into your new 401k?

you can definitely do it to consolidate accounts but keep in mind you have more access to withdraw contributions from an IRA than a 401k. Obviously you don't want to withdraw anything early but it's something to keep in mind if shite hits the fan.

Also, seems like most company 401k plans have very limited investment options so if the IRA is rather large you might not want to do it.