I recently started a job that pays $150K per year on paper(i.e. my offer letter says my yearly salary will be this) in NYC. In reality, after taxes and all the deductions, I will probably take home less than 100K. My questions is can I still contribute to Roth or traditional IRA ? If I cannot contribute IRA, what do to save for retirement ? And what happens to the contributions I have made before getting the job(i.e. do I need to move it out)?
can I still contribute to Roth or traditional IRA ?
To determine whether you can make Roth IRA contributions or deductible traditional IRA contributions, see the IRS guidance. The limits are based on your "modified adjusted gross income" and filing status for a given calendar year.
If I cannot contribute IRA, what do to save for retirement ?
Your employer may offer a 401(k) or similar plan, for which there are likely no pertinent income limits. In this case, make sure you contribute at least enough for the employer match.
You can make a nondeductible traditional IRA contribution regardless of income, and then convert it to Roth, known as a backdoor Roth IRA. This is a legal way of circumventing the Roth IRA income limits.
Of course, you can save additional money in an ordinary taxable account, aiming to benefit from tax-efficient funds and low long-term capital gain tax rates.
And what happens to the contributions I have made before getting the job(i.e. do I need to move it out)?
Nothing needs to be done regarding IRA contributions for prior years (including contributions for 2019 made by April 15, 2020) that were allowed based on your income for those years. If you already made a Roth IRA contribution for 2020 that will not be allowed with your 2020 income, you can withdraw the excess contribution. If you made a traditional IRA contribution for 2020, it may not be deductible but you may want to keep it in your IRA anyway (see backdoor Roth above).