Yes, but only under one of four circumstances, only for work tied to that circumstance, and only while it lasts. Start a competitive procurement right away and move to a competed contract as soon as the emergency or exigency ends.
A sole-source contract is allowed only when:
For large projects, document which circumstance applied, a description and expected amount, why competition wasn’t possible, how long the contract will be used, the steps you took to try to compete, and any conflicts of interest. Failing to plan the transition is not a reason to keep using a sole-source contract.
A written justification covering each of the points above, prepared when the decision was made.
Emergency (immediate threats, such as clearing roads for rescue) and exigency (urgent but not life-threatening, such as reopening a school by September) are different. Name the one that applies and set an end date.