AP TET

D. El. Ed. is Diploma In Elementary Education if you are pursuing or preparing for it then it's obvious, you already know you are preparing yourself for primary education (1 to 8). And after D.El.Ed, there is no need to do anything if you have the passion to teach kids.
D.El.Ed is a Diploma which is sufficient for teaching in elementary section. But, if you want to do more in education, I mean if you want to teach in higher classes than yes, you can need to take TET. You are eligible to do that.
Good luck.

Please check for your eligibility to appear for the TET exam from the criteria mentioned below:
Eligibility for TET exam:
1) You must be of Indian origin.
2) A graduation degree from a recognised university.
3) A B.Ed degree is also mandatory.
4) At least 50 percent marks.
5) There is no age limit to appear for the exam.
Please note that in order to pass the Teachers Eligibility Test, you will have to score at least 60 percent marks. Candidates belonging to SC/ST would need 55 percent marks to clear the exam.
Regards.

Please refer to the link to know about TSTET:
https://www.shiksha.com/teaching-education/middle-school/exams/tstet. TSTET is Telangana State Teacher Eligibility Test conducted by Department of School Education, Government of Telangana in order to shortlist candidates for appointment as teachers for Classes I to VIII in Telangana State.