An appeal "as of right" is one that is guaranteed by statute or some underlying constitutional or legal principle.
ɐn ɐpˈiːl "æz ʌv ɹˈaɪt" ɪz wˈʌn ðæt ɪz ɡˌæɹəntˈiːd baɪ stˈætʃuːt ɔːɹ sˌʌm ˌʌndɚlˈaɪɪŋ kˌɑːnstɪtˈuːʃənəl ɔːɹ lˈiːɡəl pɹˈɪnsɪpəl.