Is there a relationship between the noble verse, "Those who avoid the greater sins and immoralities, except for minor offenses," from Surat An-Najm, and the noble verse, "But whoever seeks beyond that – then it is those who are the transgressors," from Surat Al-Ma'arij?

There is no connection or contradiction between the two verses. Allah's statement: ﴿الَّذِينَ يَجْتَنِبُونَ كَبَائِرَ الإِثْمِ وَالْفَوَاحِشَ إِلَّا اللَّمَمَ﴾ [An-Najm: 32] praises those who avoid major sins and immoralities, "except for minor offenses (al-lamam)." There is a difference of opinion regarding "al-lamam," whether it refers to what occurred during the pre-Islamic era of ignorance (Jahiliyyah) or to minor sins. As for the other verse in Surahs Al-Mu'minun and Al-Ma'arij, it states that whoever seeks beyond his wife or what his right hand possesses (slave-women) for his private parts is considered an transgressor of Allah's limits. The only connection between them is the command to stay away from immoralities.