In plain words
Soon that person becomes dharmic and attains lasting peace. Son of Kunti, declare it boldly: My devotee never perishes.
Word for word
Soon he becomes one whose mind is set on dharma and attains lasting peace; O son of Kuntī, declare it: My devotee does not perish.
The commentators
Bhagavadgītābhāṣyam
उत्सृज्य च बाह्यां दुराचारतां अन्तः सम्यग्व्यवसायसामर्थ्यात् —
क्षिप्रं शीघ्रं भवति धर्मात्मा धर्मचित्तः एव । शश्वत् नित्यं शान्तिं च उपशमं निगच्छति प्राप्नोति । शृणु परमार्थम् , कौन्तेय प्रतिजानीहि निश्चितां प्रतिज्ञां कुरु, न मे मम भक्तः मयि समर्पितान्तरात्मा मद्भक्तः न प्रणश्यति इति ॥ ३१ ॥
In plain words
And having dropped the outward misconduct, then inwardly, by the sheer force of a right resolve —
Quickly, without delay, that person becomes righteous-minded, their whole mind turned toward what is right. They arrive at a peace that lasts, a stillness that never breaks. Listen closely, Arjuna, to this ultimate truth — hold it as settled, beyond doubt: My devotee, one who has surrendered their inmost self to Me, never, ever perishes.
Close to the Sanskrit
And having cast off outward misconduct, inwardly, by the power of right resolve —
Quickly, [that is,] swiftly, he becomes righteous-minded, [that is,] one whose mind is set on righteousness, indeed. He attains, [that is,] obtains, perpetual, [that is,] eternal, peace, [that is,] cessation [of turmoil]. Listen to the highest truth, O son of Kuntī: hold this as a settled declaration — My devotee, [that is,] one whose inner self is surrendered to Me, does not perish.