Hi, I just moved from the US to the UK. I made some self-employed income from Jan-March. Do I pay estimated tax on it if it's less than my standard deduction for 2019?

Are you US citizen/Resident ( Green Card ) ?  Are you planning to be there for a while ( as an employee, self-employment or as a student )?  When did you actually leave the USA ( when did you arrive abroad ) ?  Standard deduction may or may not  help answer the question.  What is your filing status ( Single, married )?  do you have your family with you ?  Their immigration status?  Do they also work ?

 Thanks for asking these qu's! I am a US and UK citizen, single, no dependants. Left USA in April, permanently. Shall work in the UK from now on, no further earning in the USA.