Silent ⟨r⟩

In standard English (in England) the letter ⟨r⟩:

• is silent if there is a consonant sound directly after.
• is silent if there is no sound directly after.
  
• is pronounced if there is a vowel sound directly after.
  

SILENT ⟨r⟩:

fork /fɔːk/
car /kɑː/
first /fɜːst/
horse /hɔːs/

PRONOUNCED ⟨r⟩:

forest /ˈfɒrɪst/
rack /rak/
merry /ˈmɛri/
pouring /ˈpɔːrɪŋ/

Linking ⟨r⟩

The silent ⟨r⟩ rule also applies to connected speech, if a word such as CAR has a silent ⟨r⟩ at the end, this ⟨r⟩ will be pronounced if the next word begins with a vowel sound:

SILENT: Is your car here? 
PRONOUNCED: Is your car electric? 

Rhotic vs Non-rhotic Accents

English accents that contain silent ⟨r⟩ are ‘non-rhotic’; these include most English accents in England, Wales, Australia, New Zealand and South Africa.

Accents in which every ⟨r⟩ is pronounced are ‘rhotic’, and these include most accents in USA, Canada, Ireland, Northern Ireland and Scotland.