Ancient greek characters do not appear with Times New Roman

Question

I'm using XeLaTeX and the polyglossia package to write text in italian and ancient greek.
My problem is that ,when I use e.g. the **CMU Serif** font, the greek text appears correctly, but ,when I change it to **Times New Roman**, some accented greek characters are not shown, although they are included in the font (e.g. in MS Word I see them with Times New Roman selected).
Here is my code:

\documentclass [11pt,a4paper,oneside]{book}

\usepackage{fontspec}                           
\setmainfont{CMU Serif}          % Replaced with "Times New Roman"
\usepackage{polyglossia}                        
\setdefaultlanguage{italian}                    
\setotherlanguage[variant=ancient]{greek}       

\begin{document}

Θουκυδίδης Ἀθηναῖος ξυνέγραψε τὸν πόλεμον τῶν Πελοποννησίων καὶ Ἀθηναίων, ὡς ἐπολέμησαν πρὸς ἀλλήλους, ἀρξάμενος εὐθὺς καθισταμένου καὶ ἐλπίσας μέγαν τε ἔσεσθαι καὶ ἀξιολογώτατον τῶν προγεγενημένων, τεκμαιρόμενος ὅτι ἀκμάζοντές τε ᾖσαν ἐς αὐτὸν ἀμφότεροι παρασκευῇ τῇ πάσῃ καὶ τὸ ἄλλο Ἑλληνικὸν ὁρῶν ξυνιστάμενον πρὸς ἑκατέρους, τὸ μὲν εὐθύς, τὸ δὲ καὶ διανοούμενον. [2] κίνησις γὰρ αὕτη μεγίστη δὴ τοῖς Ἕλλησιν ἐγένετο καὶ μέρει τινὶ τῶν βαρβάρων, ὡς δὲ εἰπεῖν καὶ ἐπὶ πλεῖστον ἀνθρώπων. [3] τὰ γὰρ πρὸ αὐτῶν καὶ τὰ ἔτι παλαίτερα σαφῶς μὲν εὑρεῖν διὰ χρόνου πλῆθος ἀδύνατα ἦν, ἐκ δὲ τεκμηρίων ὧν ἐπὶ μακρότατον σκοποῦντί μοι πιστεῦσαι ξυμβαίνει οὐ μεγάλα νομίζω γενέσθαι οὔτε κατὰ τοὺς πολέμους οὔτε ἐς τὰ ἄλλα.

\end{document}

These are the results:

CMU Serif	Times New Roman

EDIT
I noticed that it appends just on Overleaf, but not on my PC...

Answer 1

You can use a clone of Times that supports ancient Greek and one is available in TeX Live as Tempora.

\documentclass [11pt,a4paper,oneside]{book}

\usepackage{fontspec}                           
\setmainfont{Tempora}
\usepackage{polyglossia}                        
\setdefaultlanguage{italian}                    
\setotherlanguage[variant=ancient]{greek}       

\begin{document}

Il testo è in un clone di Times.

\begin{otherlanguage*}{greek}
Θουκυδίδης Ἀθηναῖος ξυνέγραψε τὸν πόλεμον τῶν Πελοποννησίων καὶ
Ἀθηναίων, ὡς ἐπολέμησαν πρὸς ἀλλήλους, ἀρξάμενος εὐθὺς καθισταμένου 
καὶ ἐλπίσας μέγαν τε ἔσεσθαι καὶ ἀξιολογώτατον τῶν προγεγενημένων, 
τεκμαιρόμενος ὅτι ἀκμάζοντές τε ᾖσαν ἐς αὐτὸν ἀμφότεροι παρασκευῇ 
τῇ πάσῃ καὶ τὸ ἄλλο Ἑλληνικὸν ὁρῶν ξυνιστάμενον πρὸς ἑκατέρους, τὸ 
μὲν εὐθύς, τὸ δὲ καὶ διανοούμενον. [2] κίνησις γὰρ αὕτη μεγίστη δὴ 
τοῖς Ἕλλησιν ἐγένετο καὶ μέρει τινὶ τῶν βαρβάρων, ὡς δὲ εἰπεῖν καὶ 
ἐπὶ πλεῖστον ἀνθρώπων. [3] τὰ γὰρ πρὸ αὐτῶν καὶ τὰ ἔτι παλαίτερα 
σαφῶς μὲν εὑρεῖν διὰ χρόνου πλῆθος ἀδύνατα ἦν, ἐκ δὲ τεκμηρίων ὧν 
ἐπὶ μακρότατον σκοποῦντί μοι πιστεῦσαι ξυμβαίνει οὐ μεγάλα νομίζω 
γενέσθαι οὔτε κατὰ τοὺς πολέμους οὔτε ἐς τὰ ἄλλα.
\end{otherlanguage*}

\end{document}

If you don't have the font installed as a system font, you can set it up by

\setmainfont{Tempora}[
  Extension=.otf,
  UprightFont=*-Regular,
  ItalicFont=*-Italic,
  BoldFont=*-Bold,
  BoldItalicFont=*-BoldItalic,
]

If you want to use Tempora just for Greek, do

\setmainfont{Times New Roman}

\newfontfamily{\greekfont}{Tempora}[
  Extension=.otf,
  UprightFont=*-Regular,
  ItalicFont=*-Italic,
  BoldFont=*-Bold,
  BoldItalicFont=*-BoldItalic,
]