Current job does not offer a 401k account. So I contributed yearly maximum to a Traditional IRA. My new job does offer a 401k plan. Can I still contribute to the new 401k for the year?
You can always contribute to the 401(k) if allowed by the plan. The amount you can contribute to 401(k) is not affected by IRA contributions.
However, contributing to 401(k) for a given year may make Traditional IRA contributions for that year not deductible. If you contribute to a 401(k) in a given year, you count as being covered by an employer plan, which means you cannot deduct Traditional IRA contributions that year unless your income is below a certain level. (If neither your nor your spouse was covered by an employer plan, there is no income limit to deducting Traditional IRA contributions.)
So for example, if you have already made Traditional IRA contributions under year 2018 (which is unlikely, since most people wait until close to the last minute, which is April of the following year, to make IRA contributions, so most people would be still contributing to 2017; but it's possible that you decided to contribute very early), and you later contribute to 401(k) in 2018, and your income is above the income limit for deducting Traditional IRA contributions when you are covered by an employer plan, then you can no longer deduct those Traditional IRA contributions that you made under year 2018. (In that case, you could take out the contribution plus earnings by the tax filing deadline for 2018 and it would count as if you didn't contribute. Or you could recharacterize it to a Roth IRA contribution (if your income is eligible to contribute) or convert it to a Roth IRA.)
I'm assuming you're eligible for a Traditional IRA deduction if you don't have a 401(k), but ineligible if you do. What matters is if your W-2 from any of your employers for that year has a check for 'Retirement plan' in Box 13. And what determines whether that box is checked or not for a 401(k) is not merely having access to one, but if "any contributions or forfeitures were allocated to your account for the plan year ending with or within the tax year" (IRS source). So if for example, you start a new job at the very end of the year and don't have time to contribute much to your 401(k), it might make sense to purposely not contribute the rest of the year to keep your Traditional IRA deduction.
As user102008 mentioned, if you end up becoming ineligible for a Traditional IRA deduction, you can possibly recharacterize your contribution to Roth (assuming you're under the income limits). Otherwise, it will become a non-deductible Traditional IRA contribution.