In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
If one performs ghusl properly after post-sex impurity with the intention to remove the impurity, then his ghusl is sufficient and he does not need to make wudu' in order to perform Prayers. However, if one takes an ordinary shower or bath without the intention of making ghusl, and perhaps without washing all the parts of the body, then wudu’ is necessary before praying.
"If, while taking a shower or bath, you washed/gargled your mouth and rinsed your nostrils then you need not to make a fresh wudu'. Your wudu' is already included in your shower or bathing if you had formulated the intention (niyyah) for the same.
If, however, you did not wash your mouth or rinse your nostrils while having your shower or bath, then you should make wudu'. The reason for this is that washing the mouth and rinsing the nostrils is part of wudu'. Therefore, in case of omitting the same, one should make wudu'. Likewise, one is advised to make wudu' if after having had a shower or a bath he/she has intentionally touched the private parts."
Moreover, the late Sheikh Sayyed Sabiq (may Allah bless his soul) states the following in his well-known book, Fiqh As-Sunnah:
"If a person performed post-sex ghusl but did not make ablution, the ghusl will suffice. `A’ishah (may Allah be pleased with her) said, “The Messenger of Allah did not perform ablution after ghusl." Ibn `Umar (may Allah be pleased with him) said to a man who had told him that he performed ablution after ghusl, "You went too far." Says Abu Bakr Ibn Al-`Arabi, "There is no difference of opinion among the scholars that ablution falls under the category of ghusl.
If the intention was to remove sexual impurity, it also includes the minor impurities, as what sexual impurity prevents is greater than what the minor impurities prevent. The smaller one falls under the greater one, and the intention for the greater one suffices."
May Allah guide you to the straight path, and guide you to that which pleases Him, Amen.
Allah Almighty knows best.