Pytest already knows which all tests to run. So maybe if we introspect the code and identify which all tests are using the methods we just changed, this can be done. What do you think?

It's possible to check through git diff as well:

Change in a method

diff --git a/tests/test_pytest_picked.py b/tests/test_pytest_picked.py
index e63dc00..c71fe1c 100644
--- a/tests/test_pytest_picked.py
+++ b/tests/test_pytest_picked.py
@@ -5,6 +5,7 @@ from pytest_picked import _affected_tests

 def test_shows_affected_tests(testdir):
     result = testdir.runpytest("--picked")
+    # bla bla bla

     assert "Changed test files..." in result.stdout.str()
     assert "Changed test folders..." in result.stdout.str()

Change in a class

diff --git a/tests/test_bot.py b/tests/test_bot.py
index 78fe572..50e6436 100644
--- a/tests/test_bot.py
+++ b/tests/test_bot.py
@@ -19,6 +19,7 @@ class TestBotConnection:
     @patch('grandma.bot.SlackClient.rtm_connect')
     def test_connect_on_slack_api(self, rtm_connect_mock, api_call_mock, bot):
         expected_user_id = 'A1B999WWW'
+        # bla bla bla

         rtm_connect_mock.return_value = True
         api_call_mock.return_value = {'user_id': expected_user_id}

I'll take a look on pytest code to check if there are other way to do it. If possible, feel free to bring examples for this discussion!

I think would be good to also run the tests that use the class/function which was modified

I hope it's not too impolite to point out 2 projects which already implement this:
https://github.com/ChrisBeaumont/smother
http://github.com/tarpas/pytest-testmon