Does calling a stored procedure implicitly start a new transaction?
Let's find out:

In session 1:

DELIMITER ;;
CREATE PROCEDURE p1() BEGIN SELECT 1; END;;
DELIMITER ;

CREATE TABLE t1 (id int unsigned auto_increment PRIMARY KEY);
START TRANSACTION;
INSERT INTO t1() VALUES ();
CALL p1();


In session 2:

SELECT * FROM t1;


which gives:


  Empty set (0.000 sec)


If the procedure call had caused the current transaction to be committed in order to start a new one, then we would have expected to see a row from the above SELECT.

So, back in session 1:

COMMIT;


And then session 2, run the SELECT again:

SELECT * FROM t1;


which now gives the expected result:

+----+
| id |
+----+
|  1 |
+----+
1 row in set (0.001 sec)


Conclusion: No, calling a stored procedure does not commit the current transaction and does not start a new transaction.