diff --git a/CHANGELOG.md b/CHANGELOG.md
index c9044488c555..ec2f72f3c362 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,10 @@
 
 ## master (unreleased)
 
+### Bug fixes
+
+* [#7063](https://github.com/rubocop-hq/rubocop/issues/7063): Fix autocorrect in `Style/TernaryParentheses` cop. ([@parkerfinch][])
+
 ### Changes
 
 * [#5976](https://github.com/rubocop-hq/rubocop/issues/5976): Remove Rails cops. ([@koic][])
diff --git a/lib/rubocop/cop/style/ternary_parentheses.rb b/lib/rubocop/cop/style/ternary_parentheses.rb
index e04b0561a282..6c93257b57b4 100644
--- a/lib/rubocop/cop/style/ternary_parentheses.rb
+++ b/lib/rubocop/cop/style/ternary_parentheses.rb
@@ -149,7 +149,8 @@ def infinite_loop?
 
         def unsafe_autocorrect?(condition)
           condition.children.any? do |child|
-            unparenthesized_method_call?(child)
+            unparenthesized_method_call?(child) ||
+              below_ternary_precedence?(child)
           end
         end
 
@@ -157,6 +158,15 @@ def unparenthesized_method_call?(child)
           method_name(child) =~ /^[a-z]/i && !child.parenthesized?
         end
 
+        def below_ternary_precedence?(child)
+          # Handle English "or", e.g. 'foo or bar ? a : b'
+          (child.or_type? && child.semantic_operator?) ||
+            # Handle English "and", e.g. 'foo and bar ? a : b'
+            (child.and_type? && child.semantic_operator?) ||
+            # Handle English "not", e.g. 'not foo ? a : b'
+            (child.send_type? && child.prefix_not?)
+        end
+
         def_node_matcher :method_name, <<-PATTERN
           {($:defined? (send nil? _) ...)
            (send {_ nil?} $_ _ ...)}
diff --git a/spec/rubocop/cop/style/ternary_parentheses_spec.rb b/spec/rubocop/cop/style/ternary_parentheses_spec.rb
index 0d25371c322c..08cc8a7936ab 100644
--- a/spec/rubocop/cop/style/ternary_parentheses_spec.rb
+++ b/spec/rubocop/cop/style/ternary_parentheses_spec.rb
@@ -110,6 +110,14 @@
       it_behaves_like 'code with offense',
                       'foo = bar && (baz || bar) ? a : b',
                       'foo = (bar && (baz || bar)) ? a : b'
+
+      it_behaves_like 'code with offense',
+                      'foo = bar or baz ? a : b',
+                      'foo = bar or (baz) ? a : b'
+
+      it_behaves_like 'code with offense',
+                      'not bar ? a : b',
+                      'not (bar) ? a : b'
     end
 
     context 'with an assignment condition' do
@@ -168,6 +176,12 @@
 
       it_behaves_like 'code without offense',
                       'foo = bar && (baz || bar) ? a : b'
+
+      it_behaves_like 'code with offense',
+                      'foo = (foo or bar) ? a : b'
+
+      it_behaves_like 'code with offense',
+                      'foo = (not bar) ? a : b'
     end
 
     context 'with an assignment condition' do
@@ -248,6 +262,10 @@
       it_behaves_like 'code with offense',
                       'foo = (bar[:baz]) ? a : b',
                       'foo = bar[:baz] ? a : b'
+
+      it_behaves_like 'code with offense',
+                      'foo = bar or (baz) ? a : b',
+                      'foo = bar or baz ? a : b'
     end
 
     context 'with a complex condition' do
@@ -255,6 +273,9 @@
                       'foo = (bar.baz?) ? a : b',
                       'foo = bar.baz? ? a : b'
 
+      it_behaves_like 'code without offense',
+                      'foo = (baz or bar) ? a : b'
+
       it_behaves_like 'code without offense',
                       'foo = (bar && (baz || bar)) ? a : b'
     end